Hiya.
If I had to...
I'd still cap max level at 20 for "class". Then, I'd totally change up the XP progression, making XP requirements significantly larger (say, +300k xp per level above 20th, so 21st would need 655,000, 22nd would need 955,000, etc). I'd list it as "Epic" for the 'class'. So you'd have Fighter/Epic 20th/2nd.
Now that that is out of the way, I'd really change it up; everyone would get 'stuff' based on their race...not class. Those things would be things that allow them to "skirt around" the rules system without actually breaking it. Those things wouldn't really be "kewl new powazz". For example, a Wood Elf might get to use his "Mask of the Wild" ability in any woodland area, regardless of obscurement; or a Tiefling might get his Darkvision increased to 120', but with the added benefit of being able to actually distinguish colors and not just shades of gray.
I'd most definitly NOT keep increaseing HD/hp, Proficiency Bonus, Stat(Feat) Addition, etc. Basically, all the "numbers" would stop at 20th. The only thing gaining more levels after 20th is going to do is enhance or slightly modify abilities you were born with (re: racially oriented stuff).
To me, this would keep within the confines of not "breaking" the balance of 5e's BA, but still account for those exceptionally rare individuals that keep on adventuring long past the point when they really should have settled down, started a family, and retired. Those types wouldn't really learn any "new tricks", they'd just increase or otherwise 'perfect' their old ones.
PS: As I read that, it strongly reminds me of the Racial Levels from Monty Cook's Arcana Unearthed book. You could gain up to 3 levels of your Race; each one making you closer and closer to the epitome of your species.
^_^
Paul L. Ming